1. Field of the Invention
The present invention concerns a method of synthesizing a finite impulse response digital filter and a digital filter obtained by this method.
2. Description of the Prior Art
Filtering to extract the wanted signal and eliminate interference is an essential operation in the field of signal processing. There is therefore an abundant literature dedicated to it.
Digital signal processing has the advantage over analog processing that it enables exact reproduction of the signals and the processing operations without any aging process intervening. For this reason the remainder of this disclosure is restricted to the field of digital filters.
Among the various types of digital filter known in themselves, a distinction is drawn between finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters.
An FIR digital filter is a time-invariant discrete linear system the output of which is determined by a weighted sum of a finite set of input samples, the weighting coefficients comprising the coefficients or weights of the filter defining its impulse response. A filter of this kind is usually called a non-recursive filter because its implementation does not require any feedback loop.
An IIR digital filter is also a time-invariant discrete linear system, but one in which the output is determined by a weighted sum of a certain number of inputs and a certain number of previous outputs of the same filter. This type of filter, the implementation of which requires a feedback loop to sample the previous outputs, is usually called a recursive filter.
FIR filters have many advantages, including digital stability and phase linearity. Also, an FIR filter is less complex to implement that an IIR filter having a comparable frequency characteristic. These considerations indicate the benefit of optimizing the design and implementation of FIR filters.
As a general rule, in synthesizing an FIR digital filter the first step is to synthesize an analog filter. The impulse response of this analog filter is then sampled to extract the coefficients of the FIR digital filter.
Existing methods of synthesizing FIR digital filters can be divided into two groups, respectively corresponding to the frequency domain and the time domain. These groups are, respectively, the so-called characteristic methods in which a frequency characteristic is imposed and a filter is calculated with a transfer function or frequency response providing the best match to the frequency characteristic, and the so-called windowing methods. Neither method gives a direct relation between the coefficients of the FIR filter in the time domain and the transfer function of the filter in the frequency domain. In the case of characteristic methods, this leads to Remez algorithms that are difficult to implement; in the case of windowing methods, performance is insufficient in most cases.
An aim of the present invention is to propose a new method of synthesizing an FIR digital filter enabling the filter characteristics to be specified simultaneously in the time domain, in order to define the complexity of the filter, and in the frequency domain, in order to define the performance of the filter.